Function of regulator gene
The regulator gene of the \(lac\) operon, i.e., \(lac\) \(i\), synthesises the repressor protein which switches off the operon. This is because the repressor binds to the operator region of DNA.
The operator has an overlapping sequence with the promoter. This inturn prevents the binding of RNA polymerase to the promoter region thereby inhibiting the transcription of the downstream structural genes.
Hence, the regulator gene acts as a repressor. Final answer
(A) Repressor